Logo image
On isometries of operator algebras
Journal article   Open access   Peer reviewed

On isometries of operator algebras

P. S MUHLY and CHAOXIN QIU
Journal of functional analysis, Vol.119(1), pp.138-170
1994
DOI: 10.1006/jfan.1994.1006
url
https://doi.org/10.1006/jfan.1994.1006View
Published (Version of record) Open Access

Abstract

We study the Banach space isometries of triangular subalgebras of C*-algebras that contain diagonals in the sense of Kumjian. Under a mild technical assumption, we prove that every isometry between two such algebras decomposes as a direct sum of a unitary multiple of an isometric algebra isomorphism and a unitary multiple of an isometric algebra anti-isomorphism. Moreover, each isometric algebraic isomorphism (anti-isomorphism) between two algebras of the type considered here extends to a C*-isomorphism (C*-anti-isomorphism) between the enveloping C*-algebras. Our hypotheses enable us to "coordinatize" the algebras under consideration, and the structure of the isometries between the algebras is expressed in terms of the coordinates.
Mathematics Functional analysis Mathematical analysis Exact sciences and technology Sciences and techniques of general use

Details

Metrics

Logo image